library("readxl")
mydata <- read_excel("wine.xlsx")
mydata
## # A tibble: 12,795 x 17
##    INDEX Purchase Cases STARS FixedAcidity VolatileAcidity CitricAcid
##    <dbl>    <dbl> <dbl> <dbl>        <dbl>           <dbl>      <dbl>
##  1     1        1     3     2          3.2           1.16       -0.98
##  2     2        1     3     3          4.5           0.16       -0.81
##  3     4        1     5     3          7.1           2.64       -0.88
##  4     5        1     3     1          5.7           0.385       0.04
##  5     6        1     4     2          8             0.33       -1.26
##  6     7        0     0    NA         11.3           0.32        0.59
##  7     8        0     0    NA          7.7           0.290      -0.4 
##  8    11        1     4     3          6.5          -1.22        0.34
##  9    12        1     3    NA         14.8           0.27        1.05
## 10    13        1     6     4          5.5          -0.22        0.39
## # … with 12,785 more rows, and 10 more variables: ResidualSugar <dbl>,
## #   Chlorides <dbl>, FreeSulfurDioxide <dbl>, TotalSulfurDioxide <dbl>,
## #   Density <dbl>, pH <dbl>, Sulphates <dbl>, Alcohol <dbl>, LabelAppeal <dbl>,
## #   AcidIndex <dbl>

TASK 1: EXPLORATORY DATA ANALYSIS and DATA PREP

summary(mydata$Alcohol)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   -4.70    9.00   10.40   10.49   12.40   26.50     653
hist(mydata$Alcohol)

mydata <- mydata[mydata$Alcohol >= 0, ]
hist(mydata$Alcohol)

mydata
## # A tibble: 12,677 x 17
##    INDEX Purchase Cases STARS FixedAcidity VolatileAcidity CitricAcid
##    <dbl>    <dbl> <dbl> <dbl>        <dbl>           <dbl>      <dbl>
##  1     1        1     3     2          3.2           1.16       -0.98
##  2    NA       NA    NA    NA         NA            NA          NA   
##  3     4        1     5     3          7.1           2.64       -0.88
##  4     5        1     3     1          5.7           0.385       0.04
##  5     6        1     4     2          8             0.33       -1.26
##  6     7        0     0    NA         11.3           0.32        0.59
##  7     8        0     0    NA          7.7           0.290      -0.4 
##  8    11        1     4     3          6.5          -1.22        0.34
##  9    12        1     3    NA         14.8           0.27        1.05
## 10    13        1     6     4          5.5          -0.22        0.39
## # … with 12,667 more rows, and 10 more variables: ResidualSugar <dbl>,
## #   Chlorides <dbl>, FreeSulfurDioxide <dbl>, TotalSulfurDioxide <dbl>,
## #   Density <dbl>, pH <dbl>, Sulphates <dbl>, Alcohol <dbl>, LabelAppeal <dbl>,
## #   AcidIndex <dbl>

Explanation: I removed the negative and zero Alcohol values as those appeared to be errors in the dat. Wine should not have a negative alcohol value.

summary(mydata$Chlorides)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -1.1710 -0.0320  0.0460  0.0543  0.1520  1.3510    1250
plot(mydata$Chlorides)

hist(mydata$Chlorides)

summary(mydata$VolatileAcidity)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -2.7900  0.1300  0.2800  0.3253  0.6350  3.6800     653
plot(mydata$VolatileAcidity)

hist(mydata$VolatileAcidity)

plot(mydata$VolatileAcidity,mydata$Chlorides)

summary(mydata$CitricAcid)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -3.2400  0.0300  0.3100  0.3101  0.5800  3.8600     653
plot(mydata$CitricAcid)

hist(mydata$CitricAcid)

summary(mydata$ResidualSugar)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
## -127.800   -1.900    3.900    5.471   16.000  141.150     1224
plot(mydata$ResidualSugar)

hist(mydata$ResidualSugar)

summary(mydata$FreeSulfurDioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -555.00   -1.00   30.00   30.68   70.00  623.00    1263
plot(mydata$FreeSulfurDioxide)

hist(mydata$FreeSulfurDioxide)

summary(mydata$Density)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.8881  0.9878  0.9945  0.9943  1.0008  1.0992     653
plot(mydata$Density)

hist(mydata$Density)

summary(mydata$TotalSulfurDioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  -823.0    28.0   124.0   121.3   208.0  1057.0    1290
plot(mydata$TotalSulfurDioxide)

hist(mydata$TotalSulfurDioxide)

summary(mydata$pH)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.480   2.960   3.200   3.206   3.470   6.130    1022
plot(mydata$pH)

hist(mydata$pH)

summary(mydata$Sulphates)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
## -3.1300  0.2800  0.5000  0.5262  0.8500  4.2400    1794
plot(mydata$Sulphates)

hist(mydata$Sulphates)

summary(mydata$AcidIndex)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   4.000   7.000   8.000   7.769   8.000  17.000     653
plot(mydata$AcidIndex)

hist(mydata$AcidIndex)

mydata=abs(mydata)

summary(mydata$Sulphates)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.0000  0.4300  0.5900  0.8462  1.0900  4.2400    1794
plot(mydata$Sulphates)

hist(mydata$Sulphates)

mydata$STARS[is.na(mydata$STARS)]=0
mydata$Purchase[is.na(mydata$Purchase)]=0
mydata$STARS
##     [1] 2 0 3 1 2 0 0 3 0 4 1 2 2 3 0 0 0 3 2 2 1 1 1 0 2 0 2 4 2 1 3 1 0 1 1 2
##    [37] 0 2 1 0 2 2 1 1 2 4 1 1 2 0 0 2 1 0 1 0 0 2 1 0 0 3 1 1 1 4 3 0 3 3 1 4
##    [73] 0 1 1 1 1 0 1 3 0 0 3 3 0 2 3 1 3 0 0 1 0 1 0 3 1 2 0 1 2 0 3 2 1 2 0 1
##   [109] 2 2 0 0 0 2 0 2 1 0 0 1 2 1 2 2 0 1 2 1 0 3 0 3 3 0 0 0 4 2 0 3 0 2 1 1
##   [145] 0 3 1 4 3 2 2 0 0 2 2 1 3 0 0 3 2 4 3 0 3 4 0 0 1 0 1 1 2 1 2 0 0 0 3 4
##   [181] 2 2 0 1 3 3 3 0 1 0 3 0 0 3 0 2 0 2 3 0 2 3 2 2 3 2 1 2 0 2 1 2 0 2 0 2
##   [217] 0 3 1 2 3 0 2 2 1 1 1 3 2 3 0 3 0 0 0 0 0 0 0 3 1 4 3 3 2 4 0 0 2 2 4 1
##   [253] 0 3 2 3 2 3 2 2 3 3 1 0 0 3 3 3 0 2 0 2 4 2 2 2 3 3 1 0 0 2 0 2 0 3 1 0
##   [289] 0 3 0 0 2 1 0 1 0 0 3 0 2 3 1 0 4 3 2 0 2 3 0 1 2 0 2 2 2 3 0 1 1 0 1 0
##   [325] 2 1 3 0 0 2 1 2 0 1 2 3 3 0 2 1 0 2 1 4 0 3 1 3 3 3 3 0 0 1 2 3 0 1 1 1
##   [361] 2 1 2 1 3 1 3 2 1 0 2 0 0 1 0 1 2 0 1 0 2 3 2 0 1 1 1 0 3 2 0 2 3 2 0 2
##   [397] 0 0 4 0 3 2 1 0 4 2 0 0 1 0 2 0 0 1 3 0 3 2 3 1 1 0 1 0 2 0 1 1 2 0 2 0
##   [433] 2 2 1 1 0 3 2 0 1 2 3 2 1 4 2 2 0 2 0 2 0 1 3 0 0 0 2 3 0 1 4 0 0 0 0 0
##   [469] 0 3 1 3 2 2 2 0 1 0 0 1 0 1 1 0 2 0 2 1 2 0 0 4 4 1 0 1 2 0 1 1 2 2 1 1
##   [505] 1 2 2 3 3 0 2 1 1 0 0 2 0 0 0 2 0 3 0 2 0 0 0 0 2 3 1 2 3 3 0 0 2 2 0 4
##   [541] 3 2 2 2 0 1 2 3 1 0 0 0 2 4 2 0 0 3 1 2 0 1 0 0 1 0 0 2 1 3 0 0 1 0 1 2
##   [577] 2 0 2 1 0 0 3 3 0 3 1 3 0 0 3 1 4 1 2 3 4 1 0 2 0 0 3 3 1 0 2 0 1 1 2 2
##   [613] 3 3 3 2 2 0 1 2 2 1 2 0 1 0 4 0 0 2 4 2 2 1 0 4 0 3 2 3 1 0 2 1 1 0 3 1
##   [649] 1 2 2 3 1 2 3 1 4 1 2 1 3 1 1 2 1 1 0 0 0 0 3 0 3 1 0 1 3 2 1 4 0 1 2 0
##   [685] 1 2 0 0 3 0 0 0 1 1 1 2 1 0 0 2 0 4 3 1 4 3 1 0 1 2 3 4 2 3 1 0 0 4 1 0
##   [721] 2 2 1 1 3 1 2 0 2 3 2 3 3 1 0 0 3 0 2 0 1 3 1 0 2 0 1 3 1 2 3 0 4 1 4 0
##   [757] 4 0 1 1 1 1 2 3 2 2 2 4 2 0 2 0 2 0 0 0 2 2 2 3 4 1 0 3 3 2 2 0 2 1 2 0
##   [793] 2 2 0 3 0 3 2 4 0 1 0 3 1 1 3 2 0 2 2 1 3 0 0 2 1 2 0 1 0 2 1 1 1 4 0 3
##   [829] 1 2 4 3 4 1 3 4 1 0 1 0 3 1 2 1 0 0 3 0 1 2 0 3 1 4 0 2 0 0 2 4 4 1 0 0
##   [865] 0 2 1 2 0 1 0 0 2 3 2 4 2 2 0 0 2 3 0 2 0 0 2 1 2 2 3 1 1 0 0 3 1 1 4 2
##   [901] 3 3 0 0 2 1 2 2 2 3 0 0 0 2 0 0 2 2 2 0 0 0 0 0 0 3 3 3 2 3 0 3 0 1 2 2
##   [937] 2 0 0 0 0 0 0 1 0 2 2 1 0 2 2 0 3 2 3 1 2 4 0 1 2 2 0 0 2 1 2 1 0 0 2 0
##   [973] 3 4 3 3 2 2 0 0 0 4 1 2 0 2 2 3 3 0 2 0 0 3 2 2 2 2 2 0 3 4 2 0 0 3 2 3
##  [1009] 0 2 0 1 0 2 0 2 2 2 2 2 2 1 0 2 4 1 0 0 1 2 0 0 4 0 2 0 0 2 0 2 0 2 1 2
##  [1045] 1 0 3 0 2 2 1 1 0 2 2 2 3 1 0 0 2 4 1 2 3 3 0 0 2 0 0 1 3 0 2 1 1 0 3 0
##  [1081] 1 1 2 1 0 4 1 1 3 0 1 2 0 4 0 3 0 1 1 1 3 0 1 0 0 0 1 2 0 3 1 2 3 0 0 0
##  [1117] 0 0 1 3 3 2 3 4 0 2 1 1 2 2 0 1 0 2 4 0 2 1 2 1 1 0 2 2 0 1 2 4 2 2 0 3
##  [1153] 2 0 0 0 2 2 1 2 1 0 2 4 0 2 1 0 2 0 2 3 0 1 2 0 1 0 0 2 2 1 0 2 1 1 0 0
##  [1189] 0 0 0 2 3 0 2 4 2 1 0 4 1 3 2 0 0 3 0 2 1 1 0 3 3 3 3 0 4 2 0 2 3 3 2 1
##  [1225] 0 3 0 0 1 1 2 4 2 3 2 2 3 0 3 1 0 2 0 3 2 0 1 3 2 0 0 2 2 2 0 2 2 0 2 0
##  [1261] 0 1 2 2 3 3 1 1 3 1 0 0 0 0 0 1 1 2 2 1 2 0 1 3 0 3 0 2 3 2 2 0 0 3 0 3
##  [1297] 0 0 1 1 2 1 3 2 2 3 0 2 4 4 2 0 2 1 1 3 0 0 2 0 1 1 1 0 2 3 1 0 2 2 2 1
##  [1333] 2 2 1 1 1 1 0 0 3 2 1 1 3 2 4 3 0 2 0 0 1 2 2 0 3 3 1 0 0 0 2 2 3 0 0 0
##  [1369] 3 1 1 1 0 0 3 2 0 0 1 3 3 2 1 0 4 1 1 1 3 0 0 1 2 2 2 4 2 2 3 0 1 3 2 0
##  [1405] 2 2 0 0 2 0 1 1 0 1 2 2 1 1 2 1 3 2 0 0 0 0 2 3 0 0 3 0 0 2 0 0 1 1 1 4
##  [1441] 4 0 2 1 4 2 4 3 0 3 0 2 0 3 1 0 0 4 2 3 2 0 2 3 3 4 2 0 0 1 4 4 1 1 0 3
##  [1477] 2 3 2 0 2 1 2 1 2 1 0 2 1 0 1 1 1 0 3 1 0 1 3 0 0 0 4 0 1 2 0 0 0 1 2 1
##  [1513] 2 4 1 1 2 0 1 0 3 2 1 0 2 1 1 2 0 1 0 3 2 2 0 2 3 2 4 2 1 3 1 2 0 0 3 1
##  [1549] 2 3 2 1 1 2 0 0 3 0 3 0 3 0 2 0 3 0 0 2 1 2 1 1 1 3 1 2 4 1 0 2 0 0 1 0
##  [1585] 1 1 2 1 1 2 3 2 1 1 1 0 0 0 1 0 2 1 0 0 2 3 1 4 3 1 0 0 3 1 1 2 1 4 1 3
##  [1621] 2 0 0 1 1 4 0 0 2 2 0 1 1 3 3 3 2 3 3 2 1 0 3 0 3 0 3 3 2 0 2 1 2 0 2 1
##  [1657] 2 2 3 0 3 3 3 2 2 2 2 2 0 0 1 1 1 0 0 0 0 4 1 0 4 0 2 2 3 2 0 2 1 2 1 0
##  [1693] 0 3 2 1 3 3 3 0 2 1 3 0 4 3 1 0 0 0 2 2 1 0 2 1 0 2 2 0 1 1 0 2 3 0 0 3
##  [1729] 2 0 2 3 3 1 1 0 3 3 1 3 2 1 2 3 1 1 2 2 2 1 3 2 0 2 2 4 3 3 3 0 2 0 0 0
##  [1765] 1 4 2 2 3 2 3 2 0 0 0 1 2 3 4 3 0 1 3 2 1 4 2 3 2 2 2 2 1 1 2 1 3 2 2 3
##  [1801] 3 3 2 0 1 3 4 1 2 0 2 2 0 3 1 1 3 0 2 1 1 2 2 0 2 0 1 3 2 0 1 2 2 4 2 2
##  [1837] 0 1 0 0 0 2 2 2 2 3 1 1 3 1 0 1 1 0 3 0 0 0 4 2 2 1 1 2 1 3 1 0 1 3 2 2
##  [1873] 1 4 0 0 0 3 1 3 2 3 2 2 2 4 0 0 3 0 0 1 2 1 3 1 3 0 3 3 1 2 1 2 1 4 0 0
##  [1909] 3 1 0 0 0 1 3 1 4 1 2 0 0 0 2 2 0 3 0 2 3 2 4 1 2 1 0 2 2 1 2 1 1 2 0 2
##  [1945] 3 2 2 0 2 3 2 2 0 1 0 0 2 3 1 2 1 0 2 1 0 3 0 3 0 0 0 0 0 3 0 1 1 2 1 0
##  [1981] 1 3 0 2 3 2 2 0 0 0 1 2 1 0 4 0 2 3 0 0 0 2 1 0 1 2 1 2 0 4 2 0 3 2 2 0
##  [2017] 1 1 1 2 3 2 3 0 3 0 1 3 1 0 3 0 3 1 3 1 3 0 2 1 0 3 3 4 4 2 2 1 2 3 0 0
##  [2053] 2 2 2 1 0 0 2 0 1 2 0 0 2 3 0 2 2 2 0 0 1 2 0 2 0 0 2 2 1 1 1 3 1 2 1 2
##  [2089] 2 3 0 4 0 0 2 0 3 0 1 0 4 0 3 0 2 3 1 2 2 3 3 2 2 0 3 0 0 0 2 3 0 0 0 1
##  [2125] 2 1 2 0 2 2 2 2 0 3 3 0 2 3 4 2 1 0 0 3 1 0 0 3 3 4 0 3 0 1 4 1 2 2 1 4
##  [2161] 2 1 0 4 0 2 2 4 3 0 1 2 3 2 1 2 3 0 3 0 2 1 0 0 0 2 2 1 0 0 3 2 3 0 3 0
##  [2197] 1 1 2 1 0 2 2 4 0 1 0 3 0 2 0 3 2 3 1 4 1 3 2 0 0 1 2 0 3 0 0 0 1 3 3 3
##  [2233] 0 2 1 1 2 3 3 1 1 1 2 1 2 0 1 1 0 0 2 2 2 1 0 3 0 1 2 3 1 0 3 1 3 1 2 3
##  [2269] 0 2 3 3 2 0 0 0 1 1 2 0 4 2 3 2 1 1 3 2 3 2 1 3 2 0 3 1 2 3 4 1 1 2 1 2
##  [2305] 2 1 1 2 2 2 3 1 3 0 0 1 0 2 1 0 3 1 1 3 2 2 3 1 0 2 1 1 2 0 0 2 0 0 2 3
##  [2341] 1 2 2 1 2 2 3 2 2 1 1 0 2 2 2 1 2 3 2 4 1 0 1 4 2 4 0 3 2 1 3 0 1 0 2 1
##  [2377] 2 0 0 3 2 4 2 0 3 2 2 3 3 0 2 3 2 2 0 1 2 1 3 2 0 0 3 0 3 2 3 2 0 1 3 2
##  [2413] 1 1 0 1 0 3 0 2 0 0 1 2 1 1 1 4 2 3 0 0 0 3 0 0 1 0 2 0 0 0 2 3 2 2 0 2
##  [2449] 0 3 2 0 0 1 3 3 1 0 0 2 0 0 1 0 0 0 2 3 2 0 2 2 2 2 1 0 0 2 0 1 3 1 3 0
##  [2485] 3 2 0 2 3 3 2 2 2 2 2 3 3 0 3 2 4 0 2 2 2 2 0 0 1 0 0 1 1 4 2 1 0 0 1 2
##  [2521] 2 0 2 0 2 0 2 2 1 3 1 0 0 0 2 3 0 0 2 0 2 1 3 3 3 2 4 0 0 2 0 0 0 0 1 1
##  [2557] 1 2 1 2 2 2 1 1 0 0 0 2 4 0 1 1 0 1 3 1 0 0 3 0 2 0 0 2 0 1 2 0 1 2 2 1
##  [2593] 3 1 1 3 2 3 4 3 2 0 4 0 0 0 0 2 0 2 3 2 2 4 1 2 2 0 0 1 2 1 0 1 3 2 0 2
##  [2629] 3 3 3 2 2 2 0 1 2 3 3 0 4 0 2 2 2 1 0 2 3 0 2 1 0 1 0 3 2 1 1 2 2 2 3 0
##  [2665] 2 0 2 2 2 0 1 1 1 0 0 0 4 3 1 3 0 1 3 3 1 3 2 2 2 0 2 1 0 1 1 3 1 1 0 1
##  [2701] 2 0 2 1 2 0 1 2 0 3 2 2 3 1 1 3 3 1 0 0 2 2 3 0 0 3 3 2 3 3 0 2 0 2 2 0
##  [2737] 3 1 4 0 1 1 3 1 1 0 2 0 2 0 2 2 3 0 1 4 1 0 0 4 1 0 2 2 2 0 2 2 2 0 2 3
##  [2773] 1 0 1 2 2 1 4 4 1 2 2 0 2 3 2 0 2 0 2 3 2 1 2 0 1 2 1 0 4 0 0 3 1 4 1 3
##  [2809] 2 2 1 3 1 0 0 1 3 1 2 2 1 2 1 2 1 0 2 1 0 0 1 0 3 2 1 0 1 0 1 3 3 2 0 4
##  [2845] 3 2 0 2 0 0 0 0 3 1 2 1 2 0 1 0 0 2 1 2 0 1 0 0 0 3 1 3 1 2 1 2 1 1 1 0
##  [2881] 0 2 2 2 2 4 1 1 1 0 0 1 0 2 3 2 2 1 2 0 3 0 4 2 3 2 3 0 2 0 3 3 0 0 1 1
##  [2917] 3 0 3 0 2 4 1 0 0 1 2 0 0 0 2 3 1 1 0 2 1 3 0 0 2 3 2 1 3 3 2 0 1 0 2 0
##  [2953] 3 1 2 2 2 0 1 2 1 1 3 2 0 1 0 1 0 1 0 3 3 1 1 3 4 2 2 0 0 2 2 0 0 0 1 1
##  [2989] 2 0 0 3 1 3 0 4 2 1 1 3 2 1 2 0 4 3 1 0 2 0 0 1 1 0 0 2 2 0 2 0 4 2 3 3
##  [3025] 3 2 4 0 2 2 1 1 0 1 3 0 3 0 2 2 3 0 0 0 2 0 0 1 3 4 3 1 2 2 0 3 2 0 2 0
##  [3061] 0 2 0 1 0 4 1 0 3 1 0 0 0 1 1 1 0 0 1 3 0 1 2 0 4 1 2 3 0 3 3 2 0 2 2 2
##  [3097] 1 2 2 0 2 1 3 0 0 0 2 2 0 2 0 0 3 3 0 3 1 3 1 0 3 2 1 1 1 3 2 3 0 3 2 0
##  [3133] 1 2 0 1 4 0 4 0 0 0 1 1 1 1 3 0 2 2 1 0 2 1 1 1 3 1 1 3 0 0 2 2 2 0 3 3
##  [3169] 3 1 1 3 1 1 1 0 1 2 0 1 3 2 2 1 1 2 0 2 3 4 3 2 1 0 2 0 3 0 2 3 3 0 1 2
##  [3205] 2 2 3 0 4 3 2 4 2 0 2 0 1 4 2 1 2 3 2 3 0 3 4 1 2 0 2 1 1 0 1 2 3 4 2 1
##  [3241] 0 2 0 2 1 1 0 0 0 3 1 1 2 2 2 1 0 4 0 2 0 2 1 2 1 2 1 0 3 0 0 2 0 3 1 0
##  [3277] 2 0 1 2 2 0 0 1 3 0 2 3 0 2 2 1 2 0 0 1 3 0 0 1 0 1 3 3 2 2 3 0 1 1 0 0
##  [3313] 3 2 1 0 2 3 0 3 3 1 1 2 0 2 2 1 0 0 1 2 1 1 4 0 1 0 4 3 2 1 2 2 2 2 4 3
##  [3349] 1 0 1 0 2 4 0 1 3 0 0 2 2 1 0 1 1 1 2 2 3 1 0 0 1 0 3 3 2 1 1 4 0 3 3 3
##  [3385] 1 0 1 0 4 0 2 0 1 0 0 1 1 0 1 1 1 0 4 0 1 2 1 1 2 1 2 2 0 2 2 2 1 2 1 3
##  [3421] 0 2 2 0 2 2 0 0 3 1 1 0 0 1 1 3 1 2 2 2 2 1 2 0 3 2 3 2 3 1 2 2 0 2 3 0
##  [3457] 2 2 2 2 1 3 2 0 2 2 2 4 3 2 2 1 1 1 0 1 1 0 2 3 3 1 0 0 0 1 2 3 2 1 2 0
##  [3493] 1 2 1 2 2 1 1 0 3 1 3 1 3 1 1 0 2 1 2 1 0 1 2 1 1 0 1 2 3 0 1 0 3 1 4 0
##  [3529] 2 2 2 2 0 0 0 3 4 2 0 2 1 0 3 2 0 2 2 3 2 2 3 4 1 1 1 0 4 0 0 1 1 1 0 1
##  [3565] 1 0 0 3 4 3 1 3 0 0 1 0 1 3 0 0 0 0 0 0 2 2 2 1 0 0 1 0 1 2 0 0 1 0 2 0
##  [3601] 0 2 1 0 0 3 0 2 1 2 0 0 0 3 0 1 1 2 3 0 0 2 2 3 2 0 2 0 4 1 2 2 1 0 0 2
##  [3637] 0 1 4 2 2 1 1 2 3 1 3 2 0 1 2 2 0 3 0 0 2 3 2 3 2 2 3 0 1 0 2 0 2 0 1 1
##  [3673] 1 0 0 0 2 0 0 2 3 4 0 0 0 3 1 1 3 3 2 1 2 2 2 3 3 3 0 4 3 3 2 2 4 2 0 4
##  [3709] 1 0 2 1 1 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 1 2 1 2 0 1 0 3 2 0 4 0 0 3 1 0
##  [3745] 2 2 1 2 4 3 1 1 0 1 2 0 0 3 1 2 2 3 2 1 3 4 3 2 2 1 1 2 1 0 1 1 2 1 0 3
##  [3781] 0 2 0 2 1 2 0 0 0 2 3 4 0 0 3 2 3 1 0 3 0 2 2 2 0 2 3 3 1 4 0 0 2 0 3 3
##  [3817] 1 1 0 0 2 2 2 2 0 0 1 0 2 0 2 3 2 0 1 3 4 0 4 0 3 1 2 1 3 2 0 2 0 0 0 2
##  [3853] 3 2 0 1 2 4 1 0 3 3 1 1 0 3 0 1 2 1 3 4 0 2 1 0 3 2 3 1 2 2 1 0 2 3 0 2
##  [3889] 0 0 0 1 1 0 1 1 2 0 3 3 0 1 1 2 0 1 0 2 2 0 2 1 2 2 4 0 2 3 2 3 0 1 4 0
##  [3925] 1 0 2 0 0 1 3 1 0 1 2 3 2 0 3 3 1 0 2 1 0 0 3 1 2 1 2 2 1 2 3 0 3 0 1 3
##  [3961] 0 0 1 2 2 2 3 1 2 1 1 0 1 1 3 0 1 1 3 2 4 0 2 2 0 0 0 0 0 0 2 2 1 3 3 2
##  [3997] 0 0 2 2 1 0 1 2 0 2 1 1 2 0 1 0 0 0 1 0 3 3 1 3 2 1 4 2 4 1 2 0 0 0 2 4
##  [4033] 2 0 0 1 1 2 0 4 1 0 3 1 0 0 1 4 1 0 3 2 2 3 2 0 1 0 2 2 1 0 0 2 0 1 0 2
##  [4069] 3 1 3 0 2 1 0 0 1 2 0 3 3 0 1 2 3 0 1 2 0 3 3 2 1 1 2 0 0 0 2 3 3 1 0 3
##  [4105] 3 3 3 3 1 3 2 3 1 1 0 2 1 2 1 3 0 2 1 3 0 0 3 1 3 3 0 0 4 2 3 2 2 1 1 3
##  [4141] 2 0 3 2 3 4 2 1 2 0 2 0 3 2 3 2 0 1 3 2 0 0 0 3 4 0 0 3 1 0 2 2 2 0 0 1
##  [4177] 0 2 0 0 2 4 0 0 2 3 2 1 3 0 2 2 0 1 3 1 3 0 1 2 1 3 0 0 3 0 2 0 2 2 3 0
##  [4213] 1 0 2 1 4 1 3 3 3 2 3 0 0 0 1 0 3 2 0 1 3 3 2 0 2 3 2 2 0 1 0 1 0 3 2 2
##  [4249] 0 0 3 0 1 4 1 2 2 1 0 2 2 2 2 1 3 2 0 2 2 1 3 2 0 1 3 2 3 0 0 2 3 4 1 2
##  [4285] 1 2 0 1 1 0 1 2 1 0 0 2 0 0 2 1 2 0 1 1 1 1 1 1 3 2 2 0 3 0 1 2 1 1 1 0
##  [4321] 2 0 0 0 3 1 0 1 0 1 1 0 1 0 2 4 0 1 0 1 1 3 3 1 0 1 2 0 0 0 4 2 0 2 0 0
##  [4357] 3 1 2 0 2 2 0 2 0 0 0 0 0 0 0 3 3 1 1 1 3 2 1 1 2 3 0 0 2 1 1 2 2 1 0 1
##  [4393] 2 0 3 0 2 2 2 3 2 1 3 4 2 0 1 1 2 0 0 1 3 1 1 0 1 1 3 1 4 3 1 2 0 0 2 1
##  [4429] 3 2 3 0 1 0 0 3 2 2 3 0 0 0 1 0 1 0 0 1 0 3 1 2 0 0 1 2 0 0 3 0 1 1 1 2
##  [4465] 4 3 0 0 0 0 1 0 0 3 0 1 2 1 0 2 0 3 1 3 2 3 2 2 2 2 0 0 3 0 0 3 3 0 2 4
##  [4501] 1 3 0 2 2 0 1 3 3 0 1 2 3 2 2 2 2 2 3 1 2 1 4 1 2 0 2 2 3 1 3 1 0 2 1 0
##  [4537] 3 2 1 1 0 2 4 3 0 2 3 0 0 1 0 3 3 2 2 3 2 1 3 2 0 4 2 1 1 0 2 1 1 1 0 1
##  [4573] 3 2 2 0 0 3 3 2 3 0 2 0 0 0 3 0 3 3 2 2 0 3 0 1 0 3 2 0 1 0 3 1 1 1 2 3
##  [4609] 2 1 0 0 0 0 4 0 0 3 3 2 1 2 1 1 4 0 0 1 1 0 1 2 4 2 3 0 1 1 3 2 3 2 3 1
##  [4645] 0 1 2 2 0 0 2 0 3 1 1 2 2 2 3 0 0 2 0 0 4 1 3 0 1 1 1 3 0 1 3 1 1 2 2 4
##  [4681] 1 2 2 1 2 0 1 2 3 0 0 3 4 1 2 1 2 1 3 2 3 1 3 2 0 4 3 2 0 1 4 0 4 0 0 1
##  [4717] 1 4 3 0 3 4 2 3 2 3 1 3 1 1 0 3 2 2 1 0 0 2 2 1 1 0 3 1 4 2 0 4 4 2 1 1
##  [4753] 1 0 3 0 2 1 2 0 1 1 0 1 0 2 0 0 1 2 1 1 1 3 3 2 3 1 1 2 3 2 3 0 3 0 0 3
##  [4789] 2 1 4 2 0 2 3 0 3 1 0 1 0 0 2 3 0 0 3 1 2 1 2 1 2 0 0 2 3 3 1 2 1 2 1 2
##  [4825] 0 0 3 0 2 2 2 1 2 0 1 1 0 3 1 2 1 1 1 1 0 0 0 2 0 2 3 3 3 3 0 2 3 0 4 1
##  [4861] 3 0 3 4 0 0 2 1 1 2 0 1 2 1 0 3 1 1 2 0 1 1 2 2 3 3 0 3 2 0 1 0 4 2 2 2
##  [4897] 0 0 0 1 0 0 3 1 0 2 0 2 0 3 1 0 2 1 4 4 2 0 0 1 0 3 0 2 1 1 3 2 1 3 3 3
##  [4933] 4 0 4 2 0 1 3 1 0 0 3 4 0 3 0 1 2 2 2 2 1 2 3 2 0 0 1 1 0 0 3 3 0 0 0 0
##  [4969] 3 4 2 2 2 1 2 3 0 1 1 0 0 3 0 0 2 2 3 1 0 0 1 2 0 1 0 3 3 0 3 1 0 1 0 0
##  [5005] 2 3 4 0 0 2 0 1 0 3 2 1 0 3 1 3 0 0 3 0 2 2 0 3 0 0 0 1 1 3 2 2 1 2 0 1
##  [5041] 1 1 0 0 3 0 0 0 0 0 1 1 2 0 1 0 2 1 2 1 4 2 2 2 2 1 0 0 1 0 3 2 0 0 2 0
##  [5077] 2 3 3 3 0 2 2 2 0 3 1 0 2 2 3 0 2 2 2 2 1 3 3 1 3 0 1 0 0 1 2 1 2 2 2 3
##  [5113] 3 3 0 1 0 0 3 0 3 1 2 0 1 1 0 3 2 1 0 0 1 2 0 4 2 1 2 2 4 1 0 0 3 4 4 2
##  [5149] 4 3 1 2 0 2 0 1 2 0 2 2 0 3 2 0 4 3 4 0 1 3 1 0 2 3 0 4 3 1 2 0 1 2 1 0
##  [5185] 0 3 1 0 0 3 2 3 2 3 3 3 0 1 3 0 3 0 0 2 2 3 3 2 1 3 2 1 2 2 3 2 2 0 2 0
##  [5221] 2 3 0 3 3 0 1 2 0 3 0 3 1 1 2 1 2 0 1 4 3 3 3 3 1 1 0 0 3 1 3 1 2 1 3 2
##  [5257] 4 1 1 2 4 3 0 2 3 2 3 3 1 2 3 0 2 1 3 0 0 0 3 1 2 2 0 0 3 1 0 1 2 2 2 2
##  [5293] 2 2 2 3 0 2 3 4 1 0 1 0 1 0 1 4 4 0 2 2 1 0 3 0 4 1 1 0 0 2 2 0 0 2 0 3
##  [5329] 0 0 3 3 0 2 0 2 2 1 0 1 0 3 1 0 0 0 3 2 0 1 0 0 3 3 0 1 2 3 3 0 1 0 2 1
##  [5365] 2 3 3 2 2 0 1 1 0 0 2 1 1 3 2 2 2 2 1 2 0 2 1 1 1 3 3 3 3 2 2 0 1 2 4 1
##  [5401] 4 0 2 1 2 1 1 0 2 0 2 1 4 0 2 2 4 2 0 1 1 2 2 0 2 0 0 1 2 0 0 2 1 3 0 0
##  [5437] 3 3 2 0 0 1 4 4 1 0 3 0 3 2 0 2 0 0 1 4 4 2 3 4 1 1 2 2 2 4 3 0 0 3 1 3
##  [5473] 2 3 3 3 2 2 2 1 0 0 2 1 1 3 1 4 0 0 1 1 2 1 0 2 0 0 2 0 0 3 1 2 2 3 3 2
##  [5509] 1 0 0 0 1 0 1 2 1 1 2 2 4 2 2 4 3 2 1 3 3 2 0 4 1 3 2 2 2 1 2 1 1 0 2 0
##  [5545] 0 3 0 1 2 3 4 1 0 0 0 1 2 3 4 0 3 2 0 0 1 3 0 1 4 0 1 1 2 3 1 1 0 1 1 2
##  [5581] 2 1 2 3 3 0 0 3 1 4 2 0 0 1 3 3 2 3 1 1 1 2 3 3 3 3 2 1 4 2 3 1 1 0 3 3
##  [5617] 3 1 3 0 1 2 2 1 3 1 4 3 0 1 0 0 1 0 0 2 3 3 3 0 0 1 1 0 1 2 3 0 0 2 1 1
##  [5653] 1 0 2 0 0 4 2 3 3 0 0 0 0 1 0 0 1 4 1 1 2 1 3 3 0 3 0 1 1 0 2 2 0 0 0 0
##  [5689] 4 1 2 0 1 2 0 1 0 1 2 1 0 1 1 2 1 0 2 1 2 2 0 2 3 2 0 2 1 0 0 0 2 2 2 2
##  [5725] 2 3 2 3 0 0 1 2 1 1 1 0 3 1 0 3 0 2 0 2 3 0 0 2 1 0 4 0 0 3 1 3 2 2 0 3
##  [5761] 1 2 2 2 2 1 1 3 0 2 2 0 3 1 2 1 2 2 1 3 1 0 1 0 0 1 0 2 0 1 2 1 0 1 1 2
##  [5797] 2 2 1 3 3 1 1 2 2 2 2 4 2 2 0 1 2 3 0 3 1 2 0 0 0 2 0 2 2 2 3 0 1 3 2 0
##  [5833] 0 2 0 0 2 2 2 1 3 2 2 1 0 0 3 0 1 2 1 1 2 1 1 2 1 0 0 0 3 1 3 0 0 2 3 1
##  [5869] 3 0 1 1 1 0 0 3 2 2 2 0 1 0 1 1 0 1 3 2 2 1 3 0 0 4 2 1 0 4 2 1 4 1 0 2
##  [5905] 2 3 3 2 1 3 0 0 0 0 0 0 0 4 2 0 0 0 2 1 4 0 3 0 0 2 1 2 0 1 1 1 0 2 4 1
##  [5941] 1 0 0 1 1 2 0 2 1 2 1 3 1 3 1 1 1 2 0 2 2 0 2 0 3 2 0 3 0 1 1 4 0 1 1 3
##  [5977] 2 3 1 0 2 0 1 2 3 3 3 2 1 1 2 0 0 0 0 0 0 1 2 1 2 3 2 2 1 1 2 1 0 0 1 2
##  [6013] 1 1 2 3 1 0 1 1 0 1 1 2 2 0 0 0 2 0 0 3 1 3 2 0 3 1 0 0 3 0 2 2 0 1 1 2
##  [6049] 0 1 2 3 3 2 3 1 2 2 0 0 2 0 0 0 2 1 3 0 0 2 0 2 2 1 0 1 0 3 3 2 2 2 2 2
##  [6085] 1 0 1 1 0 3 2 1 2 0 2 3 0 2 2 2 3 3 1 1 0 3 1 0 3 3 1 0 0 1 3 1 1 0 3 0
##  [6121] 3 2 0 0 1 3 0 1 2 1 0 2 0 2 3 4 0 1 2 4 2 2 0 0 3 2 2 1 2 2 1 3 0 3 3 1
##  [6157] 0 1 3 2 3 2 0 2 0 0 2 0 1 0 1 2 1 0 2 2 2 2 3 3 0 1 0 2 3 0 3 1 0 3 1 0
##  [6193] 3 3 2 0 3 0 2 3 1 2 0 0 3 1 2 3 0 0 2 3 1 2 1 3 2 3 1 2 1 1 2 1 0 1 0 1
##  [6229] 0 2 2 3 3 0 3 1 2 1 1 3 1 1 4 1 3 4 2 0 0 4 1 2 0 1 2 1 2 1 1 0 1 2 1 2
##  [6265] 0 2 3 1 0 3 0 0 0 2 0 2 2 0 0 3 1 0 2 1 2 3 3 3 1 4 2 2 1 0 3 3 1 3 4 3
##  [6301] 0 2 0 2 2 0 2 1 1 2 2 1 1 3 0 0 3 1 0 0 1 1 2 2 1 3 3 2 3 1 2 0 1 0 0 2
##  [6337] 0 1 3 2 2 2 0 1 1 0 2 2 0 3 2 3 0 1 1 1 2 2 1 1 0 2 2 2 2 2 3 2 0 2 1 4
##  [6373] 2 1 1 3 2 0 1 2 3 0 3 1 0 0 1 2 1 1 0 1 0 2 2 2 2 2 3 1 0 1 2 4 3 0 2 2
##  [6409] 4 0 2 0 0 0 0 1 2 3 0 3 1 2 1 2 1 2 3 0 4 4 2 2 3 0 3 0 0 0 2 1 3 2 0 3
##  [6445] 2 3 2 1 1 0 0 0 3 3 3 4 2 0 0 0 2 3 3 2 1 4 2 2 2 0 4 3 2 1 4 1 2 2 2 1
##  [6481] 0 2 2 2 0 1 2 2 3 1 0 0 1 2 1 0 1 0 4 2 1 0 0 2 0 1 1 3 1 1 3 0 3 2 2 1
##  [6517] 0 3 2 0 3 0 0 3 2 0 0 1 0 1 0 0 0 0 0 3 1 2 0 2 2 4 0 0 3 1 3 0 2 2 2 1
##  [6553] 4 2 2 1 0 1 2 0 0 3 2 1 0 1 1 1 2 2 1 3 2 1 3 1 2 3 3 3 2 0 1 2 2 2 0 3
##  [6589] 3 3 0 3 1 0 0 2 0 0 3 2 3 0 2 0 3 1 0 0 3 0 1 1 0 2 3 0 2 1 0 3 2 2 0 2
##  [6625] 3 1 0 0 1 3 3 1 3 0 2 2 2 4 3 2 2 0 0 1 1 1 3 0 3 1 0 3 2 3 0 0 0 3 2 1
##  [6661] 0 4 1 2 1 1 1 4 1 2 2 1 2 0 2 1 0 1 3 2 3 1 2 2 1 3 1 1 0 4 2 2 0 0 0 2
##  [6697] 1 3 3 0 2 0 1 2 0 2 1 0 2 2 2 0 3 3 2 0 0 4 3 2 0 1 3 2 2 2 2 1 0 4 2 0
##  [6733] 0 1 4 1 0 4 2 4 1 1 3 4 1 1 1 3 1 1 1 4 0 1 0 0 2 0 1 3 0 2 3 0 0 0 2 4
##  [6769] 2 3 3 4 0 2 0 1 0 0 1 2 1 3 1 0 4 3 3 0 2 3 0 1 0 0 2 2 4 1 1 0 1 1 2 2
##  [6805] 0 3 2 0 0 4 2 2 2 0 0 1 3 0 3 3 3 1 2 1 0 4 0 3 2 1 1 0 0 1 4 2 2 2 1 0
##  [6841] 0 0 3 0 2 0 4 2 0 2 0 0 0 3 2 1 2 1 3 1 0 2 1 1 1 4 0 2 0 2 2 2 2 1 0 2
##  [6877] 0 2 2 0 0 1 0 2 2 0 0 1 4 3 2 3 2 0 2 0 2 3 2 1 1 0 0 2 2 2 0 3 3 1 2 0
##  [6913] 3 1 0 3 1 3 1 0 1 1 1 0 1 0 2 4 3 2 0 1 3 3 0 0 3 1 0 0 0 4 2 0 0 1 3 0
##  [6949] 2 1 0 0 1 4 0 3 3 2 2 1 2 2 3 2 0 1 0 0 3 0 1 4 0 1 2 1 1 1 1 3 3 2 0 0
##  [6985] 2 0 4 0 3 2 3 0 3 3 0 2 1 0 0 4 1 3 0 1 2 2 3 0 1 3 2 0 2 3 0 1 2 4 0 0
##  [7021] 2 0 0 2 0 1 1 2 2 2 2 3 2 0 1 0 0 0 0 2 2 3 2 2 3 2 1 0 1 0 0 1 0 0 0 1
##  [7057] 1 0 2 0 4 1 1 0 2 2 0 2 3 2 2 0 0 1 0 2 0 2 3 0 1 3 0 2 0 1 1 1 0 4 0 0
##  [7093] 1 0 2 4 2 0 1 1 3 2 1 0 0 0 0 0 1 3 0 3 1 0 0 0 2 3 3 3 1 1 0 1 3 1 3 0
##  [7129] 2 3 0 0 0 2 1 4 1 2 0 1 0 0 0 2 0 0 2 3 3 1 3 0 0 1 0 3 1 2 0 3 0 3 0 0
##  [7165] 1 4 2 0 0 0 2 1 3 0 3 3 2 1 0 2 3 1 0 0 1 1 0 2 1 2 2 2 1 2 0 2 2 0 2 0
##  [7201] 1 1 2 3 0 1 1 3 0 3 1 2 1 1 1 3 2 3 1 0 3 2 3 1 2 0 2 3 2 1 0 2 3 1 0 2
##  [7237] 3 1 1 3 1 4 3 2 1 1 0 2 3 2 2 2 0 3 0 0 0 3 2 1 4 2 1 1 0 3 0 0 0 0 3 2
##  [7273] 2 0 0 3 1 2 2 0 2 3 0 0 2 0 3 3 0 1 2 0 3 2 3 2 2 2 3 0 2 3 0 2 0 0 1 0
##  [7309] 1 3 0 3 0 1 1 0 2 0 0 0 1 1 1 0 2 0 2 2 1 2 2 0 3 3 2 0 4 0 4 3 2 1 3 2
##  [7345] 2 0 1 2 0 1 2 3 1 0 2 3 3 2 2 2 1 0 2 2 1 0 1 1 1 2 2 2 1 2 3 2 1 1 2 1
##  [7381] 2 3 0 0 3 2 1 0 3 3 3 2 3 0 1 0 0 0 0 1 2 1 1 1 0 3 1 3 1 3 1 2 1 3 0 2
##  [7417] 1 0 4 3 2 1 1 1 2 1 1 0 2 4 3 2 0 0 2 2 2 0 0 2 0 2 3 0 0 2 2 2 0 2 3 1
##  [7453] 1 0 1 2 2 0 0 0 1 2 1 0 4 1 0 2 0 2 0 2 1 1 0 2 0 2 1 2 2 0 0 2 3 1 0 4
##  [7489] 1 1 4 0 2 2 2 1 2 2 2 1 4 0 0 2 1 3 0 1 0 0 2 0 2 0 3 4 4 0 0 2 2 0 1 0
##  [7525] 1 0 0 2 2 2 3 2 3 1 0 2 3 1 4 2 0 0 1 0 1 3 3 0 1 0 0 2 4 2 2 1 1 0 0 3
##  [7561] 0 0 2 2 3 1 2 3 3 2 2 1 0 2 0 2 0 4 3 0 2 0 0 0 0 0 1 3 3 1 2 0 0 1 0 1
##  [7597] 2 4 0 0 1 0 0 1 1 0 0 3 0 2 3 2 4 1 0 2 1 0 3 2 3 3 1 3 4 0 2 2 0 3 2 0
##  [7633] 4 0 3 2 2 1 0 2 3 1 2 3 1 1 1 1 2 3 0 1 0 3 0 1 2 0 1 0 2 1 2 3 0 1 0 4
##  [7669] 2 1 1 2 2 1 1 1 1 2 1 0 3 2 2 0 0 2 0 0 3 3 2 0 0 0 2 1 0 2 2 1 1 0 0 2
##  [7705] 0 1 3 1 3 3 0 2 0 1 4 1 0 0 0 2 3 0 0 2 0 4 3 2 0 1 0 0 0 0 0 0 0 0 2 0
##  [7741] 0 2 0 2 2 2 2 1 1 0 1 2 2 0 2 1 0 0 1 2 3 3 3 1 1 4 0 0 0 1 2 2 2 0 1 4
##  [7777] 1 4 2 2 3 0 2 2 3 2 2 0 3 1 0 2 1 1 1 2 3 2 1 3 3 1 2 4 0 2 4 1 1 0 3 0
##  [7813] 2 1 0 2 3 0 2 2 3 0 1 2 0 3 4 0 2 3 1 1 0 2 0 0 1 3 3 2 2 3 0 0 0 0 2 0
##  [7849] 3 1 2 0 2 2 2 2 1 1 0 1 2 2 2 3 2 1 3 3 1 3 2 0 1 2 0 0 0 2 0 3 0 3 2 2
##  [7885] 1 1 2 2 0 0 0 0 2 1 0 1 1 4 2 1 0 0 2 3 1 1 1 2 2 2 0 2 1 2 1 4 0 2 0 1
##  [7921] 2 2 2 0 1 1 1 2 1 0 0 0 1 1 3 1 2 1 1 0 3 3 1 1 3 3 1 3 3 1 2 1 0 1 2 0
##  [7957] 2 2 1 0 2 3 3 1 2 2 2 1 0 2 1 2 4 0 1 2 2 2 0 3 0 3 0 1 3 0 2 3 1 2 3 1
##  [7993] 2 4 0 1 0 1 2 2 2 2 1 0 1 1 2 4 0 2 1 1 2 0 2 0 0 0 3 0 2 1 1 0 1 2 3 2
##  [8029] 3 0 1 2 1 2 4 3 3 0 1 0 0 3 0 3 0 3 1 1 0 3 0 2 1 2 0 0 3 0 2 2 2 2 1 4
##  [8065] 3 0 2 2 0 0 1 3 0 0 0 2 0 3 2 1 1 0 0 2 1 2 0 1 2 0 2 1 0 1 2 0 1 0 3 2
##  [8101] 1 2 2 2 0 2 1 2 2 1 2 0 1 2 0 0 3 0 2 0 1 2 3 2 0 2 2 1 0 4 0 0 2 1 1 0
##  [8137] 1 3 2 4 2 0 3 0 0 1 2 0 2 2 0 1 2 3 2 3 1 1 0 1 1 2 2 3 1 2 0 3 0 2 3 0
##  [8173] 1 2 0 3 3 2 2 0 3 1 3 0 0 2 2 1 2 3 3 0 2 3 0 2 0 3 3 3 1 4 1 2 1 2 2 3
##  [8209] 2 3 1 1 1 2 0 3 0 1 0 4 2 4 1 1 1 0 1 3 2 2 2 2 2 2 0 3 3 0 3 1 0 0 0 2
##  [8245] 3 0 1 1 1 2 4 3 0 0 2 2 0 0 4 1 4 2 3 1 1 1 1 1 1 3 2 1 0 1 0 0 0 2 2 1
##  [8281] 4 2 2 0 2 1 0 2 3 0 2 0 0 0 2 0 3 2 0 2 3 0 3 0 2 2 3 0 3 0 2 2 2 2 2 1
##  [8317] 1 3 2 3 1 2 0 2 1 1 3 1 1 0 2 2 0 2 3 0 0 3 2 2 2 0 2 2 2 2 0 0 2 3 0 2
##  [8353] 2 0 1 2 0 3 3 3 1 0 1 2 0 3 2 4 0 2 0 0 4 2 0 1 2 1 1 0 0 2 0 3 1 0 2 1
##  [8389] 2 1 1 0 2 2 0 4 1 2 1 0 1 2 3 1 0 2 3 4 0 0 2 0 0 0 0 2 0 0 3 1 2 2 1 1
##  [8425] 3 0 2 2 1 3 0 1 4 1 3 2 2 0 2 1 2 0 0 1 3 1 0 0 3 0 2 0 1 3 0 3 0 2 1 0
##  [8461] 2 0 2 0 1 3 3 4 1 1 0 3 0 0 2 3 1 1 2 3 2 1 0 1 3 2 1 2 1 2 0 1 3 3 3 2
##  [8497] 0 1 0 1 1 1 2 0 0 0 0 1 2 3 1 0 3 3 2 1 2 2 3 2 0 3 1 0 4 2 2 0 2 3 3 3
##  [8533] 2 3 0 0 0 4 3 2 0 3 3 0 3 2 2 3 0 2 0 1 4 0 3 0 2 1 0 2 3 2 0 3 0 1 0 0
##  [8569] 0 4 0 4 3 0 1 0 0 2 4 1 0 3 2 0 0 3 0 3 2 0 3 0 0 3 4 2 0 2 0 1 0 2 0 2
##  [8605] 0 4 0 3 0 0 1 1 0 2 2 2 2 2 0 2 1 1 0 2 0 1 0 1 0 3 3 1 1 2 3 0 0 0 2 0
##  [8641] 0 1 0 0 1 3 3 1 2 1 0 2 2 3 0 2 1 0 0 2 2 2 0 0 0 2 0 2 2 1 3 2 2 0 1 2
##  [8677] 2 2 1 2 2 2 0 2 2 1 2 0 3 2 1 1 1 2 2 1 1 0 0 0 0 1 1 3 3 2 2 2 0 2 0 1
##  [8713] 2 1 3 1 0 3 2 1 0 1 1 2 3 0 0 3 1 0 0 0 1 1 0 2 2 0 3 1 2 2 0 2 0 0 4 0
##  [8749] 0 1 0 3 3 0 2 3 1 0 2 2 0 2 0 4 1 0 0 3 4 3 3 2 1 0 1 1 4 0 0 1 3 3 3 2
##  [8785] 0 3 4 0 0 0 3 2 3 1 0 3 0 0 3 0 2 2 3 2 0 0 1 1 4 1 3 0 2 0 3 2 2 1 2 3
##  [8821] 3 0 2 1 4 2 1 2 0 0 2 2 2 3 4 1 0 1 1 0 2 3 1 1 3 0 0 1 2 2 3 2 2 3 2 2
##  [8857] 2 0 1 0 1 3 4 3 0 2 0 0 0 1 3 0 0 2 2 0 0 0 0 1 3 1 2 0 2 2 3 2 4 0 0 4
##  [8893] 0 3 1 3 2 1 0 0 1 4 3 3 0 4 0 0 3 1 2 2 1 4 2 1 1 1 1 2 1 1 2 0 2 2 0 0
##  [8929] 1 0 0 2 0 0 1 0 0 3 0 3 2 1 3 0 2 1 1 1 1 0 2 0 1 0 3 2 1 4 1 1 0 3 3 2
##  [8965] 1 1 0 3 0 0 3 1 2 2 3 1 2 4 3 2 1 1 2 2 2 2 2 2 2 4 2 2 1 2 1 3 0 0 1 2
##  [9001] 3 0 1 1 1 2 3 2 2 3 0 2 0 1 2 2 1 0 1 3 3 0 3 0 2 0 1 0 1 1 0 0 2 1 0 1
##  [9037] 3 1 0 3 1 2 3 3 3 0 0 1 1 0 0 1 1 3 0 0 0 0 4 2 4 1 2 1 1 2 2 3 4 2 1 2
##  [9073] 2 1 4 2 3 4 0 3 0 0 2 0 1 3 0 2 0 4 1 0 0 2 3 0 3 3 1 3 0 2 0 0 2 2 1 0
##  [9109] 3 2 1 2 1 2 1 2 1 1 2 3 0 0 1 3 3 1 3 0 0 0 2 3 2 3 0 1 3 3 0 0 0 1 1 3
##  [9145] 0 3 3 0 2 1 3 0 3 0 1 2 2 0 2 2 0 2 0 0 2 2 2 4 2 1 1 0 0 0 0 2 0 1 2 2
##  [9181] 3 1 0 1 2 2 1 1 2 3 1 3 1 0 1 0 3 0 3 2 3 3 1 2 0 3 1 3 1 3 1 0 1 0 0 1
##  [9217] 0 2 3 3 0 1 2 3 1 1 3 2 3 1 1 2 3 4 3 2 0 3 0 2 0 1 0 3 2 0 1 0 0 3 3 2
##  [9253] 1 2 2 2 0 2 2 1 1 2 2 1 2 0 3 3 3 2 0 2 0 0 2 1 0 3 0 1 1 3 2 0 0 2 2 1
##  [9289] 3 4 3 0 3 0 2 0 3 0 2 2 1 2 0 4 3 3 2 1 1 2 0 0 1 2 0 1 2 2 3 1 0 0 3 2
##  [9325] 0 1 4 1 3 2 0 1 0 2 2 4 1 2 1 1 1 2 3 2 1 1 3 0 1 1 1 0 1 0 3 1 0 3 1 1
##  [9361] 2 2 0 1 1 1 0 4 0 0 2 2 2 2 3 4 2 2 2 0 0 0 2 0 2 3 0 3 2 0 1 0 0 1 0 0
##  [9397] 2 0 2 2 2 0 1 0 0 2 3 2 3 1 2 3 3 3 4 3 1 1 2 1 2 2 2 1 2 1 3 1 0 0 1 0
##  [9433] 2 3 0 3 1 0 2 2 2 0 3 3 2 0 3 2 1 2 0 1 2 1 1 2 2 1 1 1 2 3 0 4 4 2 3 2
##  [9469] 2 2 3 2 4 0 3 0 0 2 1 2 0 0 3 0 1 3 0 3 3 0 0 4 1 0 3 0 3 1 4 0 0 1 1 1
##  [9505] 1 3 2 1 0 1 0 0 1 2 0 0 2 1 1 2 0 3 3 1 0 0 2 2 1 1 0 0 0 1 0 2 2 1 3 2
##  [9541] 0 1 0 2 3 3 3 2 1 0 1 0 0 3 0 3 2 1 2 0 4 3 3 0 1 2 1 0 2 2 0 0 1 0 0 0
##  [9577] 1 0 0 1 0 1 2 2 2 1 3 3 0 0 0 2 1 2 0 1 3 0 0 0 1 0 3 3 2 0 3 0 0 0 3 2
##  [9613] 0 1 2 3 1 1 2 2 0 1 0 3 1 2 0 3 3 2 2 4 2 0 1 0 3 2 0 1 0 0 0 1 0 2 4 1
##  [9649] 0 0 2 1 0 1 0 3 0 4 2 2 1 0 1 2 3 2 0 2 1 0 2 1 2 2 0 0 1 2 0 2 4 0 1 4
##  [9685] 0 3 4 1 0 0 2 3 0 0 1 0 0 1 3 0 2 2 3 3 2 2 1 2 0 0 1 3 2 3 1 1 1 2 0 2
##  [9721] 0 3 0 1 1 0 0 1 3 2 2 1 2 0 0 0 0 0 2 2 2 2 4 0 2 2 3 2 0 1 3 0 1 0 0 2
##  [9757] 0 0 1 3 2 1 1 2 3 1 0 0 4 3 2 3 0 3 4 1 0 3 0 0 2 0 2 0 2 0 2 2 2 3 0 4
##  [9793] 0 0 2 1 3 3 1 0 2 1 1 3 4 1 2 1 0 1 3 1 1 0 0 0 0 1 0 2 2 0 0 0 0 0 2 1
##  [9829] 0 2 1 1 0 0 3 0 0 1 1 0 0 2 1 0 1 3 0 1 0 2 1 0 3 2 0 2 3 1 1 2 4 1 2 3
##  [9865] 2 0 2 1 3 3 2 2 0 1 4 1 0 1 4 0 2 2 2 1 2 3 0 4 2 3 2 0 0 0 0 0 0 2 3 0
##  [9901] 0 1 0 1 1 0 1 3 2 4 4 2 3 0 4 0 3 2 0 1 1 2 1 1 0 2 2 0 2 0 4 2 4 0 2 0
##  [9937] 0 2 3 3 2 0 1 0 1 3 3 2 1 0 2 2 2 3 2 0 2 4 0 0 1 3 2 0 0 2 2 2 3 2 1 1
##  [9973] 2 0 2 1 1 3 0 4 1 1 0 1 1 0 1 2 1 0 2 1 2 3 1 1 1 3 3 0 2 0 3 3 3 4 1 0
## [10009] 4 1 4 1 0 1 2 4 2 0 3 3 3 2 0 0 1 2 0 0 3 0 0 2 0 3 2 0 1 2 2 2 2 0 2 2
## [10045] 2 2 1 0 2 2 2 2 2 1 0 0 0 0 1 0 1 3 0 3 2 1 1 0 1 2 2 0 3 3 2 0 0 2 0 2
## [10081] 3 3 3 3 2 0 0 4 1 0 1 3 0 1 3 0 0 4 3 0 2 2 0 0 0 2 3 1 0 2 3 2 2 1 1 0
## [10117] 1 3 0 2 1 0 0 3 0 1 2 2 0 0 3 1 2 2 0 0 1 2 0 0 1 4 3 2 2 0 2 1 0 1 1 0
## [10153] 0 1 0 0 3 3 4 1 3 0 2 0 0 2 4 0 2 4 2 3 1 0 2 2 3 4 2 2 3 4 2 0 3 0 0 1
## [10189] 2 2 3 3 2 3 3 0 0 0 3 0 2 2 1 3 0 2 3 2 1 3 0 2 0 0 0 2 0 0 2 0 2 2 1 0
## [10225] 1 0 0 0 3 4 1 1 0 1 2 3 0 1 3 2 4 2 1 1 1 2 3 2 1 2 4 3 2 3 0 3 0 1 1 2
## [10261] 4 2 2 0 3 2 2 1 2 3 1 1 2 2 1 0 2 3 3 2 3 1 1 1 2 1 2 0 2 0 3 3 1 0 3 3
## [10297] 0 3 2 3 1 1 0 0 2 0 2 3 0 2 0 3 4 3 0 1 1 0 3 0 2 2 0 4 1 4 0 0 0 0 0 2
## [10333] 1 0 1 2 1 2 3 2 1 0 0 3 1 0 0 0 0 0 0 0 2 0 1 2 0 0 2 0 1 2 4 1 2 1 3 0
## [10369] 3 3 2 0 1 1 2 3 1 2 0 3 2 2 0 3 0 1 0 0 2 4 2 0 0 0 2 2 1 1 0 0 2 2 2 0
## [10405] 0 4 0 0 1 2 3 2 2 2 1 2 1 2 1 3 2 0 0 2 3 3 0 2 0 2 3 2 3 0 0 2 3 2 3 0
## [10441] 2 3 1 2 0 2 2 2 2 1 0 0 1 2 3 0 1 1 0 2 2 3 3 1 2 1 0 1 4 0 1 0 0 0 1 0
## [10477] 0 1 1 2 2 2 3 3 0 3 1 0 4 2 0 1 3 2 2 2 0 0 2 3 0 1 2 2 1 2 2 0 1 0 1 1
## [10513] 1 0 2 0 2 3 2 0 0 1 3 1 1 3 2 2 2 0 0 1 1 1 1 0 2 2 0 2 0 0 0 1 0 3 2 0
## [10549] 0 2 4 1 1 2 2 1 4 1 1 0 0 1 0 0 4 0 3 2 2 2 0 3 2 1 3 1 2 0 1 2 2 2 1 1
## [10585] 4 2 0 3 0 2 2 0 3 3 2 1 0 1 0 1 4 0 3 1 0 1 1 0 3 3 3 0 2 0 1 2 1 4 1 1
## [10621] 1 0 2 3 1 1 1 2 2 2 1 3 2 1 2 1 2 1 2 0 2 0 1 1 1 3 0 1 2 3 1 2 1 3 0 1
## [10657] 3 0 3 3 0 4 0 2 3 0 3 0 4 0 0 0 1 0 3 1 3 4 0 0 0 3 0 1 2 1 1 0 1 2 3 2
## [10693] 1 0 1 2 1 3 1 1 3 2 1 1 2 0 1 2 0 1 1 2 0 3 2 0 0 0 0 1 1 1 1 1 2 1 0 0
## [10729] 2 0 0 3 3 0 0 0 0 0 1 0 2 0 4 0 0 0 0 1 0 4 1 1 1 0 1 2 1 0 2 2 3 0 0 2
## [10765] 3 2 1 0 4 1 3 0 1 1 3 4 2 1 0 0 1 1 2 3 1 2 3 2 1 2 2 2 0 3 2 1 4 3 1 0
## [10801] 1 0 2 3 3 3 2 0 2 0 0 3 2 1 0 0 0 0 2 1 2 0 1 0 2 3 0 3 4 2 0 0 0 2 0 0
## [10837] 1 3 2 2 2 0 4 4 0 0 0 2 2 1 2 0 0 3 1 0 1 0 1 1 2 1 1 2 3 2 3 2 2 0 0 1
## [10873] 1 3 2 2 0 0 3 0 1 4 3 0 0 1 0 0 1 3 0 3 1 2 2 0 1 0 0 0 1 2 1 0 1 4 0 0
## [10909] 1 2 1 0 0 2 2 0 1 4 2 2 2 1 0 1 1 3 1 2 2 3 0 4 0 2 3 1 0 0 0 0 1 2 2 3
## [10945] 2 0 3 2 2 2 1 2 1 2 4 3 2 2 1 1 0 2 2 1 0 0 1 2 1 1 3 2 1 1 1 3 2 0 0 0
## [10981] 2 2 1 2 1 1 2 0 3 1 3 3 4 0 3 3 0 2 0 1 3 0 3 2 3 2 0 2 3 3 3 0 1 3 0 0
## [11017] 2 1 3 1 0 1 0 0 0 2 3 3 3 1 0 2 2 4 2 0 1 0 0 0 1 3 0 2 3 0 2 3 0 3 3 0
## [11053] 2 2 2 3 1 1 1 3 4 1 0 0 2 2 2 1 1 2 0 0 2 0 1 2 2 1 2 0 4 2 0 3 0 3 0 3
## [11089] 0 1 4 4 0 1 4 2 3 1 3 2 0 2 0 2 3 2 2 1 0 3 1 0 0 0 1 1 0 0 0 2 0 2 0 1
## [11125] 0 2 0 1 3 0 2 1 2 1 2 3 0 0 0 2 0 2 1 3 1 0 1 0 0 1 1 1 3 2 0 2 0 1 3 2
## [11161] 0 0 1 2 2 1 0 2 3 2 1 1 0 0 1 2 2 0 1 1 1 2 2 2 1 0 2 1 0 2 2 1 3 3 4 2
## [11197] 0 0 0 4 1 2 2 2 1 1 2 0 2 3 2 2 4 2 0 2 1 2 2 0 3 1 0 4 2 3 0 1 0 0 0 1
## [11233] 2 2 3 1 2 1 2 2 2 2 2 2 0 3 0 1 0 3 1 0 1 0 3 1 0 2 1 3 1 2 2 1 2 2 0 1
## [11269] 3 0 3 1 2 3 1 2 1 1 4 2 1 1 1 3 2 0 3 1 0 0 2 1 1 3 4 0 1 2 0 1 1 0 2 2
## [11305] 3 2 2 0 3 0 1 1 1 1 4 3 1 0 0 1 0 0 2 3 0 3 3 2 1 2 3 0 1 3 0 3 0 3 0 0
## [11341] 2 0 0 0 1 0 0 3 0 3 0 2 0 2 2 2 2 0 0 0 0 3 2 1 1 1 0 4 0 2 1 2 3 0 3 2
## [11377] 0 0 2 1 0 0 1 2 2 1 0 0 3 0 2 1 1 0 2 1 2 2 3 2 4 1 2 2 3 0 3 4 0 4 2 0
## [11413] 0 0 0 2 0 1 0 0 0 0 1 0 0 3 2 3 0 0 2 0 0 2 3 1 0 2 0 1 2 3 0 2 0 3 2 2
## [11449] 2 1 1 3 0 0 3 2 1 2 0 0 1 2 0 3 1 1 3 1 3 0 0 2 0 2 2 1 0 0 2 4 0 2 2 2
## [11485] 2 3 2 0 1 0 0 0 2 2 2 1 2 3 3 1 1 0 0 4 1 0 4 0 0 0 0 0 0 3 2 2 0 1 3 3
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## [12241] 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0
## [12277] 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0
## [12313] 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1
## [12349] 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1
## [12385] 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0
## [12421] 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0
## [12457] 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0
## [12493] 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1
## [12529] 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1
## [12565] 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1
## [12601] 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1
## [12637] 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1
## [12673] 0 0 1 1 1

Explanation: I replacces th NA values in Purchased and STARS with zeros in order to keep enough data entries and have a value for the ones that did not.

summary(mydata$TotalSulfurDioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##     0.0   100.0   154.0   204.3   262.0  1057.0    1290
plot(mydata$TotalSulfurDioxide)

hist(mydata$TotalSulfurDioxide)

summary(mydata$TotalSulfurDioxide)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##     0.0   100.0   154.0   204.3   262.0  1057.0    1290
plot(mydata$TotalSulfurDioxide)

hist(mydata$TotalSulfurDioxide)

mydata=mydata
mydata <- subset (mydata, select = -INDEX)

TASK 2: MODELING

I will be conducting my model on the Purchase variable, which would make my models be logistic models since the response variable is binomial.

My first model is just a test:

model1=glm(mydata$Purchase~mydata$FixedAcidity+mydata$VolatileAcidity+mydata$CitricAcid, family='binomial')
model1
## 
## Call:  glm(formula = mydata$Purchase ~ mydata$FixedAcidity + mydata$VolatileAcidity + 
##     mydata$CitricAcid, family = "binomial")
## 
## Coefficients:
##            (Intercept)     mydata$FixedAcidity  mydata$VolatileAcidity  
##                1.65051                -0.02499                -0.25791  
##      mydata$CitricAcid  
##                0.04063  
## 
## Degrees of Freedom: 12023 Total (i.e. Null);  12020 Residual
##   (653 observations deleted due to missingness)
## Null Deviance:       12480 
## Residual Deviance: 12400     AIC: 12410
summary(model1)
## 
## Call:
## glm(formula = mydata$Purchase ~ mydata$FixedAcidity + mydata$VolatileAcidity + 
##     mydata$CitricAcid, family = "binomial")
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.9381   0.6136   0.6578   0.7089   1.0753  
## 
## Coefficients:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept)             1.650511   0.056005  29.471  < 2e-16 ***
## mydata$FixedAcidity    -0.024993   0.004317  -5.790 7.04e-09 ***
## mydata$VolatileAcidity -0.257911   0.038028  -6.782 1.18e-11 ***
## mydata$CitricAcid       0.040628   0.037344   1.088    0.277    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 12483  on 12023  degrees of freedom
## Residual deviance: 12404  on 12020  degrees of freedom
##   (653 observations deleted due to missingness)
## AIC: 12412
## 
## Number of Fisher Scoring iterations: 4

My second model runs on all of the response variables. However, this includes the Cases variable, which should be ommitted because if there are cases, it has obviously been purchased. Although this is the best model, as seen with the lowest AIC value, it doesn’t do us quite that much in terms of telling us whether or not the wine has been purchased. We need to focus on the other variables.

model2=glm(Purchase~.,data=mydata, family='binomial')
## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
model2
## 
## Call:  glm(formula = Purchase ~ ., family = "binomial", data = mydata)
## 
## Coefficients:
##        (Intercept)               Cases               STARS        FixedAcidity  
##         -2.297e+01           4.294e+01          -1.641e-01          -3.086e-03  
##    VolatileAcidity          CitricAcid       ResidualSugar           Chlorides  
##          2.286e-01          -1.140e-02          -3.120e-03           2.112e-01  
##  FreeSulfurDioxide  TotalSulfurDioxide             Density                  pH  
##         -4.974e-04           5.135e-04          -1.451e-01          -1.390e-01  
##          Sulphates             Alcohol         LabelAppeal           AcidIndex  
##         -4.421e-02          -3.789e-02           1.107e+00          -7.931e-03  
## 
## Degrees of Freedom: 8596 Total (i.e. Null);  8581 Residual
##   (4080 observations deleted due to missingness)
## Null Deviance:       8860 
## Residual Deviance: 8.656e-07     AIC: 32
summary(model2)
## 
## Call:
## glm(formula = Purchase ~ ., family = "binomial", data = mydata)
## 
## Deviance Residuals: 
##        Min          1Q      Median          3Q         Max  
## -3.734e-05   2.100e-08   2.100e-08   2.100e-08   1.192e-04  
## 
## Coefficients:
##                      Estimate Std. Error z value Pr(>|z|)
## (Intercept)        -2.297e+01  3.678e+04  -0.001    1.000
## Cases               4.294e+01  1.998e+03   0.021    0.983
## STARS              -1.641e-01  1.603e+03   0.000    1.000
## FixedAcidity       -3.086e-03  1.985e+02   0.000    1.000
## VolatileAcidity     2.286e-01  1.524e+03   0.000    1.000
## CitricAcid         -1.140e-02  1.489e+03   0.000    1.000
## ResidualSugar      -3.120e-03  3.690e+01   0.000    1.000
## Chlorides           2.112e-01  3.875e+03   0.000    1.000
## FreeSulfurDioxide  -4.974e-04  8.164e+00   0.000    1.000
## TotalSulfurDioxide  5.135e-04  5.798e+00   0.000    1.000
## Density            -1.451e-01  3.636e+04   0.000    1.000
## pH                 -1.390e-01  1.457e+03   0.000    1.000
## Sulphates          -4.421e-02  1.401e+03   0.000    1.000
## Alcohol            -3.789e-02  2.683e+02   0.000    1.000
## LabelAppeal         1.107e+00  1.391e+03   0.001    0.999
## AcidIndex          -7.931e-03  6.218e+02   0.000    1.000
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 8.8598e+03  on 8596  degrees of freedom
## Residual deviance: 8.6560e-07  on 8581  degrees of freedom
##   (4080 observations deleted due to missingness)
## AIC: 32
## 
## Number of Fisher Scoring iterations: 25

This model 4 is run without Cases and STARS. It has significantly improves from my first test model, as seen by the AIC.

model4=glm(Purchase~FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=mydata,family="binomial")
model4
## 
## Call:  glm(formula = Purchase ~ FixedAcidity + VolatileAcidity + CitricAcid + 
##     ResidualSugar + Chlorides + FreeSulfurDioxide + Density + 
##     pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, family = "binomial", 
##     data = mydata)
## 
## Coefficients:
##       (Intercept)       FixedAcidity    VolatileAcidity         CitricAcid  
##         7.2761837         -0.0013163         -0.2147829          0.0960032  
##     ResidualSugar          Chlorides  FreeSulfurDioxide            Density  
##         0.0004444         -0.1860454          0.0002738         -1.5246228  
##                pH          Sulphates            Alcohol        LabelAppeal  
##        -0.1958777         -0.1517309          0.0007085         -0.0295854  
##         AcidIndex  
##        -0.4481867  
## 
## Degrees of Freedom: 9053 Total (i.e. Null);  9041 Residual
##   (3623 observations deleted due to missingness)
## Null Deviance:       9319 
## Residual Deviance: 8652  AIC: 8678
summary(model4)
## 
## Call:
## glm(formula = Purchase ~ FixedAcidity + VolatileAcidity + CitricAcid + 
##     ResidualSugar + Chlorides + FreeSulfurDioxide + Density + 
##     pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, family = "binomial", 
##     data = mydata)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.3648   0.4420   0.5696   0.6810   2.4412  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        7.2761837  1.0280751   7.077 1.47e-12 ***
## FixedAcidity      -0.0013163  0.0054322  -0.242 0.808531    
## VolatileAcidity   -0.2147829  0.0464507  -4.624 3.77e-06 ***
## CitricAcid         0.0960032  0.0458782   2.093 0.036388 *  
## ResidualSugar      0.0004444  0.0010829   0.410 0.681514    
## Chlorides         -0.1860454  0.1122715  -1.657 0.097499 .  
## FreeSulfurDioxide  0.0002738  0.0002512   1.090 0.275711    
## Density           -1.5246228  1.0123853  -1.506 0.132075    
## pH                -0.1958777  0.0398495  -4.915 8.86e-07 ***
## Sulphates         -0.1517309  0.0394776  -3.843 0.000121 ***
## Alcohol            0.0007085  0.0076481   0.093 0.926189    
## LabelAppeal       -0.0295854  0.0430535  -0.687 0.491971    
## AcidIndex         -0.4481867  0.0199514 -22.464  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9319.1  on 9053  degrees of freedom
## Residual deviance: 8651.7  on 9041  degrees of freedom
##   (3623 observations deleted due to missingness)
## AIC: 8677.7
## 
## Number of Fisher Scoring iterations: 4

Model5 is close to the final model. We included the STARS variable in this model, since it is allowed. The AIC has improved even more.

model5=glm(Purchase~STARS+FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=mydata,family="binomial")
model5
## 
## Call:  glm(formula = Purchase ~ STARS + FixedAcidity + VolatileAcidity + 
##     CitricAcid + ResidualSugar + Chlorides + FreeSulfurDioxide + 
##     Density + pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, 
##     family = "binomial", data = mydata)
## 
## Coefficients:
##       (Intercept)              STARS       FixedAcidity    VolatileAcidity  
##         3.9662770          1.9719815          0.0009698         -0.1760123  
##        CitricAcid      ResidualSugar          Chlorides  FreeSulfurDioxide  
##         0.0816683          0.0013079         -0.0707479          0.0003133  
##           Density                 pH          Sulphates            Alcohol  
##        -0.1662829         -0.2128037         -0.1634135         -0.0251893  
##       LabelAppeal          AcidIndex  
##         0.0867849         -0.4025495  
## 
## Degrees of Freedom: 9053 Total (i.e. Null);  9040 Residual
##   (3623 observations deleted due to missingness)
## Null Deviance:       9319 
## Residual Deviance: 5571  AIC: 5599
summary(model5)
## 
## Call:
## glm(formula = Purchase ~ STARS + FixedAcidity + VolatileAcidity + 
##     CitricAcid + ResidualSugar + Chlorides + FreeSulfurDioxide + 
##     Density + pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, 
##     family = "binomial", data = mydata)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.93120   0.03934   0.19291   0.49787   2.50295  
## 
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)        3.9662770  1.2846839   3.087  0.00202 ** 
## STARS              1.9719815  0.0502262  39.262  < 2e-16 ***
## FixedAcidity       0.0009698  0.0069488   0.140  0.88901    
## VolatileAcidity   -0.1760123  0.0591098  -2.978  0.00290 ** 
## CitricAcid         0.0816683  0.0560160   1.458  0.14486    
## ResidualSugar      0.0013079  0.0013543   0.966  0.33417    
## Chlorides         -0.0707479  0.1411495  -0.501  0.61621    
## FreeSulfurDioxide  0.0003133  0.0003109   1.008  0.31362    
## Density           -0.1662829  1.2660135  -0.131  0.89550    
## pH                -0.2128037  0.0498256  -4.271 1.95e-05 ***
## Sulphates         -0.1634135  0.0501253  -3.260  0.00111 ** 
## Alcohol           -0.0251893  0.0095277  -2.644  0.00820 ** 
## LabelAppeal        0.0867849  0.0534034   1.625  0.10415    
## AcidIndex         -0.4025495  0.0251545 -16.003  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 9319.1  on 9053  degrees of freedom
## Residual deviance: 5570.9  on 9040  degrees of freedom
##   (3623 observations deleted due to missingness)
## AIC: 5598.9
## 
## Number of Fisher Scoring iterations: 6

This was an analysis of how well the STARS variable does when predicting Purchased. It is one of the more powerful variables when analyzed, coming close to the AIC of model4 on its own. However, when compared via VIF values, we can see when connected with other variables it imporves theri relationsips with the Purchase variable as well:

modelSTARS=glm(Purchase~STARS, data=mydata, family='binomial')
modelSTARS
## 
## Call:  glm(formula = Purchase ~ STARS, family = "binomial", data = mydata)
## 
## Coefficients:
## (Intercept)        STARS  
##     -0.7484       2.1816  
## 
## Degrees of Freedom: 12676 Total (i.e. Null);  12675 Residual
## Null Deviance:       14380 
## Residual Deviance: 8473  AIC: 8477
summary(modelSTARS)
## 
## Call:
## glm(formula = Purchase ~ STARS, family = "binomial", data = mydata)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.6986  -0.8802   0.2305   0.6541   1.5072  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -0.74840    0.03354  -22.31   <2e-16 ***
## STARS        2.18156    0.04257   51.24   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 14378.6  on 12676  degrees of freedom
## Residual deviance:  8472.9  on 12675  degrees of freedom
## AIC: 8476.9
## 
## Number of Fisher Scoring iterations: 6
set.seed(123)
mydata$u <- runif(n=dim(mydata)[1],min=0,max=1)

# Create train/test split;
train.df <- subset(mydata, u<0.70);
test.df  <- subset(mydata, u>=0.70);
names(train.df)
##  [1] "Purchase"           "Cases"              "STARS"             
##  [4] "FixedAcidity"       "VolatileAcidity"    "CitricAcid"        
##  [7] "ResidualSugar"      "Chlorides"          "FreeSulfurDioxide" 
## [10] "TotalSulfurDioxide" "Density"            "pH"                
## [13] "Sulphates"          "Alcohol"            "LabelAppeal"       
## [16] "AcidIndex"          "u"
intmodel=glm(Purchase~1,data=train.df,family='binomial')
fullmodel=glm(Purchase~STARS+FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=train.df,family="binomial")
library(car)
## Loading required package: carData
sort(vif(fullmodel),decreasing=TRUE)
##         AcidIndex      FixedAcidity             STARS                pH 
##          1.070661          1.051920          1.021914          1.011627 
##           Alcohol       LabelAppeal        CitricAcid   VolatileAcidity 
##          1.010173          1.010026          1.004295          1.003612 
## FreeSulfurDioxide     ResidualSugar         Chlorides           Density 
##          1.003531          1.003516          1.003350          1.003201 
##         Sulphates 
##          1.002005
library(car)
sort(vif(model4),decreasing=TRUE)
##         AcidIndex      FixedAcidity                pH        CitricAcid 
##          1.048841          1.037940          1.006466          1.003812 
##           Density         Sulphates           Alcohol         Chlorides 
##          1.002932          1.002468          1.002014          1.001725 
## FreeSulfurDioxide     ResidualSugar   VolatileAcidity       LabelAppeal 
##          1.001158          1.001124          1.001097          1.000553

In model2, we can see how the CASES and STARS variables are the most correlating. Still, we will use the fullmodel above as our predictive model, due to its best performance without the Cases variable.

sort(vif(model2),decreasing=TRUE)
##              STARS              Cases          AcidIndex        LabelAppeal 
##           1.207231           1.153729           1.129980           1.091676 
##      ResidualSugar            Alcohol       FixedAcidity                 pH 
##           1.083325           1.081673           1.074755           1.054502 
##         CitricAcid  FreeSulfurDioxide          Sulphates TotalSulfurDioxide 
##           1.054299           1.053398           1.043387           1.036325 
##            Density    VolatileAcidity          Chlorides 
##           1.032968           1.026442           1.023629

We can se our training model has a performance accuracy of around 79.2% in the table below, performin quite well.

library(rvest)
trainProb <- fullmodel %>% predict(train.df, type = "response")
trainPrediction <- ifelse(trainProb > 0.5, 1, 0)
table(train.df$Purchase, trainPrediction, dnn = c("Purchase", "Predict"))
##         Predict
## Purchase    0    1
##        0  822  496
##        1  467 4560

Our test set model performa almost as well at 76.2% accuracy.

testProb <- fullmodel %>% predict(test.df, type = "response")
testPrediction <- ifelse(testProb > 0.5, 1, 0)
table(test.df$Purchase, testPrediction, dnn = c("Purchase", "Predict"))
##         Predict
## Purchase    0    1
##        0  357  231
##        1  178 1943
plot(model5)

TASK 3: CONCLUSIONS AND REFLECTIONS

This assignment allowed me to sort of test what I ghave learned in this class however I wanted to. I felt most comfortable using linear models, so I decided to work on the logistic models to gain an even better understanding for it. It also seemed to be a bit simpler to work with since I would be working with binomial values. In terms of wine, I learned that the Acid levels, Alcohol content, and Label APpeal had the most influence on the purchase decision, as well as of course the amount of Stars is received. The better presented and reviewed the wine, the more likely it is to be bought. The most important parts when it comes to modeling is preprocessing the data, making sure it is usable and makes sense. Negative values for the amount of it within the wine would not make sense, so it was good to assume the absolute value of the entries, which would make a lot more sense. Next is to figure out what type of model would work best with what you are trying to predict. This was a great assignment to really test your ability on how to model data on your own.